# ex2_reg.m

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This code is a MATLAB script for logistic regression with regularization. It is divided into two main parts: Part 1: Regularized Logistic Regression In this part, the code reads in a dataset of microchip test results (two features) and their corresponding binary pass/fail labels. The data points are plotted and the user is prompted to press enter to continue. Next, polynomial features are added to the dataset. A cost function for regularized logistic regression is computed and displayed. Part 2: Regularization and Accuracies In this part, different values of lambda (the regularization parameter) are tried (0, 1, 10, 100). For each value of lambda, the decision boundary is plotted along with the training set accuracy. Now let's break down the code line by line: The first few lines are just comments describing the script and its purpose. clear; close all; clc clears the workspace, closes all plot windows, and clears the command window. data = load('ex2data2.txt'); loads the data from the ex2data2.txt file into the variable data. X = data(:, [1, 2]); y = data(:, 3); separates the input features X and output labels y from the loaded data. plotData(X, y); generates a scatter plot of the input features X and output labels y. hold on; holds the current plot so that additional elements can be added to it. xlabel('Microchip Test 1'); ylabel('Microchip Test 2'); adds x- and y-axis labels to the plot. legend('y = 1', 'y = 0'); adds a legend to the plot. hold off; releases the hold on the current plot. X = mapFeature(X(:,1), X(:,2)); maps the input features X to a higher dimensional feature space using polynomial features up to degree 6 (implemented in the mapFeature function). initial_theta = zeros(size(X, 2), 1); initializes the initial values of the model parameters theta. lambda = 1; sets the regularization parameter lambda to 1. [cost, grad] = costFunctionReg(initial_theta, X, y, lambda); computes the cost and gradient of the regularized logistic regression model with the given inputs. fprintf('Cost at initial theta (zeros): %f\n', cost); prints the cost of the model with initial parameters set to zero, including the computed regularization term. pause; prompts the user to press Enter to continue. The next several lines are comments describing Part 2. initial_theta = zeros(size(X, 2), 1); re-initializes the initial values of the model parameters theta. lambda = 1; sets the regularization parameter lambda to 1. options = optimset('GradObj', 'on', 'MaxIter', 400); sets options for the optimization algorithm used to fit the model. [theta, J, exit_flag] = fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options); finds the optimal values of the model parameters theta using the fminunc optimization function. The @(t) indicates that the following anonymous function will take one input argument t, corresponding to theta. The exit_flag variable is a scalar output indicating whether the optimization terminated successfully (0) or not (nonzero). plotDecisionBoundary(theta, X, y); plots the decision boundary of the trained model along with the input data points. hold on; holds the current plot so that additional elements can be added to it. title(sprintf('lambda = %g', lambda)); adds a title to the plot indicating the regularization parameter used. xlabel('Microchip Test 1'); ylabel('Microchip Test 2'); adds x- and y-axis labels to the plot. legend('y = 1', 'y = 0', 'Decision boundary'); adds a legend to the plot. hold off; releases the hold on the current plot. p = predict(theta, X); predicts the output labels p for the input features X using the trained model parameters theta. fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100); computes and prints the accuracy of the trained model on the training set. pause; prompts the user to press Enter to continue. Additional sets of lines follow that are similar to the ones described